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<p>In this study, we introduce two finite-dimensional Lie-Poisson Hamiltonian systems related to the Manakov equation through the nonlinearization method. Additionally, we apply the separation of variables on the common level set of Casimir functions to analyze these systems, which are related to the non-hyperelliptic algebraic curve. Ultimately, we construct the action-angle variables for these systems based on the Hamilton-Jacobi theory and derive the Jacobi inversion problem for the Manakov equation.</p>

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Action-Angle Variables for the Lie-Poisson Hamiltonian Systems Associated with the Manakov Equation

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Xue Geng,
  • Liang Guan

摘要

In this study, we introduce two finite-dimensional Lie-Poisson Hamiltonian systems related to the Manakov equation through the nonlinearization method. Additionally, we apply the separation of variables on the common level set of Casimir functions to analyze these systems, which are related to the non-hyperelliptic algebraic curve. Ultimately, we construct the action-angle variables for these systems based on the Hamilton-Jacobi theory and derive the Jacobi inversion problem for the Manakov equation.